Comments on Moore-Method TeachingMike Reed

You asked me to comment upon my experiences with Moore-method teaching as a student at Auburn and in my subsequent career.

I only considered being a mathematician after having Jo (Ford) Heath's Moore-method course in algebra. I only made the decision after having your course in topology. Growing up in rural Alabama, I had no concept of mathematics as a profession. I had loved plane geometry. I went to my teacher and asked, "What is it that I can do that is like this? "Her answer was to be an engineer. In Alabama, engineers went to Auburn, hence to Auburn I came. I quickly changed to physics seeking a more theoretical study. I took Jo's course and rediscovered the thrill of proving a theorem for myself. I took your course and finally found "what I could do that was like this."

Had I had more knowledgeable training in high school or had been an undergraduate at Princeton, I would perhaps have made the same discoveries and decisions under any teaching method. However, I am convinced that only the Moore-method would have caught me with my background in Alabama. The Moore-method showed me the thrill of discovery, the excitement of competition, and the warmth of an intellectual community. Most importantly, it provided me with the confidence that I could do original work.

Of course, Auburn at the time that I was a student was a unique Moore-method experience. With the large number of Moore-trained Texans on the faculty and the arrival of Moore's last students to join our group upon his retirement, Auburn became the new Camelot for a few shining moments. Distinguished visitors were commonplace. Sharing Tex-Mex food and beer with Mary Ellen Rudin, RH Bing, F.B. Jones, and even Kuratowski was a normal part of graduate student life in topology. We had the best of two worlds: inheriting a world-renowned mathematical tradition and creating our own identity. Competition was first-rate; access to mathematical power structures was easily available, and the social atmosphere was as good as it gets. The image of graduate school forever fixed in my mind is one of doing mathematics on napkins while sitting half-drunk on your floor at some ungodly hour in the morning; sobering up only by the need to win the argument against my fellow students.

In the novel "Lost Horizons" by James Hilton, the High Lama asks the English hero whether Shangri-La is not unique in his experience, and if the Western world could offer anything in the least like it. The Englishman answers with a smile, "Well, yes-to be quite frank, it reminds me very slightly of Oxford." Several years ago, upon joining an Oxford college, while sitting at High Table and eating a five-course, two-wine, candelabra and crystal dinner surrounded by world-class academics from many disciplines, someone asked me if I had ever encountered anything like this in America. I replied that it did remind me a bit of Auburn.

On the first day at my first national meeting of the American Mathematical Society as a graduate student, I had breakfast with Bing, a former AMS president, tea with Gail Young, the then current MAA president in his suite during a council meeting, and spent much of the evening discussing my research with Mary Ellen Rudin. Three years after my Ph.D., I found myself living in Warsaw sharing an office with Borsuk and Kuratowski. I had the opportunities because of the Moore tradition, and I had the confidence and the ability to take advantage of them because of the Moore-method teaching at Auburn.

Over the last twenty-odd years, I have often considered how to repay the debts of my mathematical youth. I have tried Moore-method teaching at Ohio University, the US Naval Academy, and at Oxford University. The experience has been varied, rewarding, and often exasperating.

At Ohio University, I naively tried at first to recreate my experience at Auburn. Without a significant infrastructure, it is almost impossible to fit a Moore-method undergraduate sequence into the established order. It was difficult, especially for a young Assistant Professor, to convince Yankee colleagues on the immense benefit of ignorance. Finally, I discovered that it was possible to have freedom in the teaching of either the very smart (i.e., honors programs) or the "considered-to-be" very dumb (i.e., education and business students). I suppose the theory was that both were in the minority and neither could be hurt too badly. Among the former, I had a student who went on to get a Ph.D. and spend time as a postdoc at the Institute for Advanced Study. Among the latter, I had two of the most memorable students of my teaching career. One was a black, handicapped Haitian who became wonderfully turned on to mathematics, got a Masters at Ohio University, and went on to do graduate work at SUNY at Buffalo. The other, although equally enthusiastic, lacked a high level of ability. However, I still proudly remember the time at 2:00 in the morning when he awoke me on the phone to tell me his first original proof of a non-trivial theorem. When I think of the joy of mathematics, it is in that voice on the phone.

At the Naval Academy, there was zero opportunity to structure a Moore-method course. However, the students were very, very bright. They were also fiercely competitive. Hence, I discovered that if I staged a series of challenge theorems with a bottle of wine to the winner, I got the same effect.

At Oxford University, the problem has been the British cultural aversion to public competition. One does not admit to wanting to beat the socks off one's fellow student. A subtle put-down is fine, but to win through a public display of effort is just not done. Of course the students are brilliant, extremely well-trained, and have normal American desires for total victory under the facade; the trick is to destroy the layers of civilization on top. I found the best approach to be proving theorems in a real-time joint effort without any attempt at competition, and leaving the counterexample to be found individually. Since I have always considered the counterexamples the best bit anyways, this has caused me no problems. To be honest, I find that this interactive style is very much to my liking. It works because the students are so good.

My conclusions are that Moore-method teaching must be adapted to (1) the nature of the institution, (2) the culture of the students, and (3) the personality of the teacher. The bottom line is that Moore-method teaching from Socrates to Moore to Fitzpatrick is about the ethical responsibility and the joy of intellectual individualism within a community of scholars.

I was sitting in a cafe last week in Warsaw, drinking beer and wine with topologists I have known for over twenty years, including a fellow graduate student, Judy Kennedy, from my days at Auburn. We were talking of mathematics and teaching. It occurred to me then that, "this is not only what I do, this is who I am." And indeed, I am who I am because I found teachers and a method of teaching that invited and challenged me to join this very particular and very special community of scholars.